Exercises of Chemical Reaction kinetics
k
2
1. The reaction A  B 
C, (1). derive the expression for formation of B in term of k1,
k
1
k2 and [A]0 by LAPACE transform method. (2).show that the maximum concentration of B
 k2 
 /( k 2  k1 ) . (3). If k1=10-8s-1 and k2=1s-1, estimate the time t、 when the
 k1 
occurs at tmax= ln 
concentration of B reaches 0.9[B]max.，What is the implications of this result.
k1

2. In the reaction A  B
 C , the equilibrium is subjected to a small disturbance and the
k2
system relaxes to a new equilibrium position where the concentrations of A, Band C are [A]e,
[B]e and. [C]e respectively, derive the expression of the relaxation time, τ in term of k1, k-1,
[A]e, [B]e and. [C]e
k
1

k2


k 1
k 2
3. Derive rate equation of the reaction A B C by determinant (matrix) method
4. In the reaction between A and B the variation of half-life of A with initial concentrations of A
and B is given in the following table
[A]0 /mol.dm-3
[B]0
/mol.dm-3
T1/2 /min.
(1). Show differential rate equation
(2). What is the rate constant
0.01
0.01
0.02
0.500
0.250.
0.250
80
160
80
R=k[A]2[B]
5. Evaluate the activation energy of the reaction CH3-H + CF3 → CH3 + H-CF3 by BEBO
method. Bond length: CH3-H, r1s = 1.09Ả H-CF3, r2s = 1.095Ả, H3C-CF3 r3s = 1.54Ả..
Bond energy: CH3-H, D1s = 105.5KCal.mol-1, H-CF3, D2s = 107.0KCal.mol-1 , H3C-CF3 D3s =
84.4KCal.mol-1 . Morse parameter : β3= 1.94Ả-1, L-J parameter: ELJ(Ne-He) = 38.0 Cal.mol-1，
rm(Ne-He) = 2.99 Ả. Calculate the potential energies, V(n2) for n=0, 0.1, 0.2, 0.3, 0.4, 0.45,
0.5 and plot the variation of potential energy with n2
6. The experimental activation energies for reaction C2H5 + H2 → -C2H6 + H have been
reported(Can. J. Chem., 60,3039(1982)): 350-550K, 50KJmol-1, 800-1100K, 71
≠
≠
KJmol-1.Eveluate the parameters m and E b for k=ATmexp(-Eb /RT)
7. Evaluate the pre-exponential factors A for gas-phrase reactions
(1) mono-atomic molecule + diatomic molecule →linear activated complex.
(2) linear poly-atomic molecule + non-linear poly-atomic molecule→non-linear activated
complex
≠
8. Evaluate ΔS for gas-phrase diamolecuar reaction at 573K, A=7.4×1010dm3 mol-1s-1,
standard state:1mol.dm-3
9. Evaluate k2/k-1 when ku=80%k∞ and [M]+10-4mol.L-1for unimolecular reaction. The
k1

*
Lindemann’s mechanism: A  M 

 A  M
k 1
,
k2
A* 
P
10. Rate constants for gas-phrase dimerization of cyclic pentylenes and the bimer decomposition
at 373K are as follows:
Dimerized: k2=106.1exp(-16700x4.184/RT)dm3mol-1s-1
Decomposed: k1=1013.1exp(-35000x4.184/RT)s-1
≠
Evaluate ΔS for forward and back reaction. What activated complex is shown?
11. The expression of k for the unimolecular reaction at 500K is k =5.2×1014exp(43700×
4.184//RT)s-1. how many degees ,S of vibrational freedom are there at least if ku is still equal
to k∞ at P=150mmHg? Derivation with RRK theory. The cross sectional area σAA= (1.0nm)2,
molecular weight, mA=160
12. Derivate the rate constant of unimolecular reaction at high pressure limit with kRRKM,
theory.
13. The decomposition reaction of acetaldehyde is CH3CHO → CH4 + CO. The reaction
mechanism is listed below:
Initial
CH3CHO → CH3•+ CHO•
Propagation CH3•+ CH3CHO → CH4 + CH3• + CO
Termination 2CH3• → C2H6
(1). Determine the production rate of CH4 with the steady state approximation for the CH3
intermediate.
(2). Evaluate the activation energy for the initial step., when the activation energies for the
overall reaction, the propagation step and termination step are given, Eexp=192.5, Ep=33.5,
ET=0KJmol-1, respectively.
14. Suggest plausible mechanism for the thermal decomposition of acetone
1.CH3COCH3 → CH3CO• + CH3•
84Kcalmol-1
2. CH3CO• → CH3• + CO
16
3. CH3• + CH3COCH3 → CH4 + CH2COCH3•
15
4. CH2COCH3• → CH3• + CH2CO
48
5. CH3• + CH2COCH3 → C2H5COCH3
5
(1). Derive the expression for the thermal decomposition rate equation of acetone in terms of
ki(i=1-5) and [CH3COCH3]
(2). Estimate the activation energy of the overall reaction.
15. The mechanism for the reaction H2 + Br2→ 2HBr is as follows:
Br2 → 2Br•
E0=192KJmol-1
Br• + H2 → HBr + H•
E1=72KJmol-1
H• + Br2 → HBr + Br•
E2=5KJmol-1
H• + HBr →H2 + Br•
E-1=5KJmol-1
2Br• → Br2
ET=0KJmol-1
Estimate the activation energy of the overall reaction Eexp. when
(1). In the initial
(2). In the end
16. (1) Derive the expression for the rate equation of the overall reaction H2 + I2→ 2HI. The
mechanism :
k
I2
1



k 1
I• + H2
2I•
k2




k
2
fast
H2I•
k3
H2I• + I• 
2HI
fast
slow
(2). What is the expression if the mechanism:
k0
I2 
2I•
k1
I• + H2 
HI + H•
k2
H• + I2 
HI + I•
kT
2I• 
I2